Hyperbolic extensions of free groups from atoroidal ping-pong
Abstract
We prove that all atoroidal automorphisms of Out(FN) act on the space of projectivized geodesic currents with generalized north-south dynamics. As an application, we produce new examples of non virtually cyclic, free and purely atoroidal subgroups of Out(FN) such that the corresponding free group extension is hyperbolic. Moreover, these subgroups are not necessarily convex cocompact.
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